Domain growth in long-range Ising models with disorder

Recent advances have highlighted the rich low-temperature kinetics of the long-range Ising model (LRIM). This study investigates domain growth in an LRIM with quenched disorder, following a deep low-temperature quench. Specifically, we consider an Ising model with interactions that decay as $J(r) \sim r^{-(D+\sigma)}$, where $D$ is the spatial dimension and $\sigma > 0$ is the power-law exponent. The quenched disorder is introduced via random pinning fields at each lattice site. For nearest-neighbor models, we expect that domain growth during activated dynamics is logarithmic in nature: $R(t) \sim (\ln t)^{\alpha}$, with growth exponent $\alpha >0$. Here, we examine how long-range interactions influence domain growth with disorder in dimensions $D = 1$ and $D = 2$. In $D = 1$, logarithmic growth is found to persist for various $\sigma > 0$. However, in $D = 2$, the dynamics is more complex due to the non-trivial interplay between extended interactions, disorder, and thermal fluctuations.